Answer:
Energy = 752.88 kJ/mol
Explanation:
The force of attraction can be written as:
[tex]F=\frac {K\times |Z_{cation}|e\times |Z_{anion}|e}{r^2}[/tex]
Integrating to find the expression for energy. We get that:-
[tex]E=\frac {K\times |Z_{cation}|e\times |Z_{anion}|e}{r}[/tex]
Where,
K is the Coulomb's constant having value 9×10⁹ N. m²/C²
[tex]Z_{cation}[/tex] is the charge on the cation
[tex]Z_{anion}[/tex] is the charge on the anion
e is electronic charge = Charge of the electron = Charge on proton [tex]1.602\times 10^{-19}\ C[/tex]
r is the distance between the cation and anion = 185.00 pm
Also, 1 pm = 10⁻¹² m
So, r = 185×10⁻¹² m
[tex]Z_{cation}=Z_{anion}=1[/tex]
Applying in the equation,
[tex]E=\frac{9\times 10^9\times 1.6\times 10^{-19}\times 1.6\times 10^{-19}}{185\times 10^{-12}}=1.25\times 10^{-18}\ J/atom[/tex]
Also,
1 atom = [tex]6.023\times 10^{23}\ mole^{-1}[/tex]
So,
Energy = [tex]1.25\times 10^{-18}\times 6.023\times 10^{23}\ J/mole=752875\ J/mole[/tex]
Also, 1 J = 0.001 kJ
So, Energy = 752.88 kJ/mol
The ionization energy of the atom from Coulomb's law is -753 KJ/mol.
From Coulomb's law;
E = Kq1q2/r
Where;
E = Electrostatic potential energy
K = 9 × 10^9 Nm^2C-2
q1 = charge on the proton = 1.6 × 10^-19 C
q2 = charge on the electron = -1.6 × 10^-19 C
r = distance of separation = 185 × 10^-12 m
Substituting the values; 9 × 10^9 Nm^2C-2 × 1.6 × 10^-19 C × -1.6 × 10^-19 C/185 × 10^-12 m
= -1.25 × 10^-18 J
To convert to KJ/mol;
-1.25 × 10^-18 J/ 1 × 10^3 × 6.02 × 10^23/1 mol
= -7.53 × 10^2 KJ/mol or -753 KJ/mol
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